15x^2+30x-27=0

Solution for 15x^2+30x-27=0 equation:

15x^2+30x-27=0

a = 15; b = 30; c = -27;
Δ = b2-4ac
Δ = 302-4·15·(-27)
Δ = 2520
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{70}}{2*15}=\frac{-30-6\sqrt{70}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{70}}{2*15}=\frac{-30+6\sqrt{70}}{30}
$